Problem $2$: Forces $F_1=5000lbf$ and $F_2=8000lbf$ are exerted on the shaft shown in the figure, which rotates at $1000re\frac{v}{m}in$ and a steady torque of $9500$ lbf $.$in being transmitted the shaft between the points of application of the forces. Use a $1050$ CD steel. The critical section of the shaft is at point $B.$ Find the minimum factor of safety for fatigue based on infinite life using the modified$-$Goodman criterion. If the life is not infinite, estimate the number of cycles and the life in hr $.$ Be sure to check for yielding. Use the properties of materials $S_{ut}=100$ksi,$S_y=84$ksi and $S_e=25\mathrm{.}6$ksi. All dimensions are in inches.